Question

use the equation of the line of best fit, ( y = 0.97x + 7.93 ), to answer the questions below. give exact answers, not rounded approximations. (a) for an increase of one year of experience, what is the predicted increase in the hourly pay rate? (b) what is the predicted hourly pay rate for a cashier who doesnt have any experience? (c) what is the predicted hourly pay rate for a cashier with 5 years of experience?

Explanation:

Step1: Find the slope

The equation of the line is \(y = 0.97x+7.93\), and the slope \(m = 0.97\). For part (a), the increase in hourly pay rate for one - year increase in experience is the slope of the line. So when \(x\) (years of experience) increases by \(1\) (\(\Delta x=1\)), using the formula \(y = 0.97x + 7.93\), if \(x_1=x\) and \(x_2=x + 1\), then \(y_1=0.97x+7.93\) and \(y_2=0.97(x + 1)+7.93=0.97x+0.97 + 7.93\). The difference \(y_2 - y_1=(0.97x+0.97 + 7.93)-(0.97x+7.93)=0.97\).

Step2: Calculate for \(x = 0\)

For part (b), when the cashier has no experience (\(x = 0\)), substitute \(x = 0\) into the equation \(y=0.97x + 7.93\). Then \(y=0.97\times0+7.93=7.93\).

Step3: Calculate for \(x = 5\)

For part (c), when \(x = 5\), substitute \(x = 5\) into the equation \(y=0.97x + 7.93\). Then \(y=0.97\times5+7.93=4.85+7.93 = 12.78\).

Answer:

(a) \(\$0.97\)
(b) \(\$7.93\)
(c) \(\$12.78\)